Strategic Effects and Incentives in Multi-issue Bargaining Games

10) if δ₂ increases v₂ increases, while v₁ decreases (increases) if

λ₁ [(1 - δ₁δ₂)² - α₂λ₂ (1 - δ₁)(δ₁ (1 + δ₂²) - 2δ₂)] + α₁δ₁ (1 - δ₁ ) > 0(< 0 respect.) (19)

Corollary 1 does not include a discussion of the first equilibrium defined in proposition
1, since this is strictly related to the outcome of a standard one-cake bargaining game
(given that player 1 is able to extract the entire surplus at the initial stage). Corollary
1 shows that the interactions of the discount factors (αi ,δj) are an important feature of
the interplay of forces in this game. When the between-cake discount factor increases
for the first mover (α1), that is, player 1 discounts less strongly the payoff obtained
in the second stage, this is not always good news for such a player (see point 1 of
Corollary 1). First of all, player 1 makes a larger concession at the first stage (x₁
decreases) to facilitate the initial agreement. Obviously, player 2’s payoff increases
when he obtains a larger share of the first division. However, player 1’s payoff, v₁,
increases only if, in the within-stage negotiations, player 1 is more patient than his
opponent (δ1 > δ2). In other words, player 1’s concession at the first bargaining stage
is too large if he fears a rejection more than his opponent does. This is an interesting
feature of the bargaining game since being more patient is often associated with a
higher payoff, but in this game this is not necessarily true, it depends on the link
between the within-cake discount factors.

A similar effect on the equilibrium outcome can also be shown when, in the
between-stage negotiations, the first responder becomes more patient (α₂ increases,

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